Answer: The correct option is (D) [tex]y=-\dfrac{3}{4}x.[/tex]
Step-by-step explanation: We are given to find the equation of a straight line passing through the points (4, -3) and (0, 0).
We know that the slope of a line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
So, the slope of the given line is
[tex]m=\dfrac{-3-0}{4-0}=-\dfrac{3}{4}.[/tex]
Since the line passes through the point (0, 0), so its equation will be
[tex]y-0=m(x-0)\\\\\Rightarrow y=-\dfrac{3}{4}x.[/tex]
Thus, the required equation of the given line is [tex]y=-\dfrac{3}{4}x.[/tex]
Option (D) is CORRECT.
